I am sorry to announce that John Nelder died on Saturday 7th August in Luton & Dunstable Hospital, where he was recovering from a fall. John was very active even at the age of 85, and retained the strong interest in our work – and statistics generally – that we will all remember with deep affection. On 13 May 2010 I took him to the Numerical Algorithms Group’s 40^{th} Anniversary Celebration near Oxford, where he was pleased to catch up with many old friends from his time on their Technical Policy Committee. Then, on 4 July 2010, he entertained Youngjo Lee, Yudi Pawitan, Mike Kenward, James Roger and myself to lunch – and to some challenging statistical discussions. However, he was becoming increasingly frail and it was a shock but perhaps, in retrospect, not a surprise to hear that he had died peacefully in his sleep.

If you would like to leave messages of condolence below, I will pass them on to his family.

John Ashworth Nelder was one of the most influential statisticians of his generation, whose work will continue to have an important and widespread effect on statistical analysis.

John was born on 8 October 1924 in Dulverton, Somerset, UK. He was educated at Blundell’s School and at Sidney Sussex College, Cambridge where he read Mathematics (interrupted by war service in the RAF) from 1942-8, and then took the Diploma in Mathematical Statistics.

Most of John’s formal career was spent as a statistician in the UK Agricultural Research Service, later renamed Agricultural and Food Research Service (AFRC), and now Biotechnology and Biological Sciences Research Council (BBSRC). His first job, from October 1949, was at the newly set-up Vegetable Research Station, later renamed National Vegetable Research Station (NVRS), and now Horticultural Research International, Wellesbourne. Then, in 1968, he became Head of the Statistics Department at Rothamsted, and continued there until his first retirement in 1984. The role of statistician in AFRC was very conducive for John, not only because of his strong interests in biology (and especially ornithology), but also because it allowed him to display his outstanding skill of developing new statistical theory to solve real biological problems. So, for example at NVRS, John developed the theory of *general balance* to provide a unifying framework for the wide range of designs that are needed in agricultural research (see Nelder 1965). Then, at Rothamsted, he developed the theory of *generalized linear models* with the late Robert Wedderburn, to overcome the problems of analysing response variables like counts and proportions that do not come from Normal distributions; see the citation classic Nelder & Wedderburn (1972) or the book by McCullagh & Nelder (1989).

This idea of directing statistical research at real biological problems began with the two earlier Heads of Statistics at Rothamsted, R.A Fisher and F. Yates, to whom John became such a worthy successor. However, John emphasized an important additional aspect, namely that the new theory should be implemented in widely-distributed statistical software to enable it to become widely used in practice.

The initial aim for John’s first statistical program, GenStat, was to provide analysis of variance for generally balanced designs. The underlying ideas took shape in 1965–1966 when John visited the Waite Institute of the University of Adelaide to work with Graham Wilkinson, who was then on secondment there from CSIRO (Commonwealth Scientific and Industrial Research Organization). More intensive development began in 1968 when John joined Rothamsted, and the wider statistical and computing expertise available at Rothamsted allowed him to develop GenStat as a truly general-purpose statistical system. GenStat continues in widespread use today, and is distributed by VSN International to users in more than 120 countries. I was honoured to take over leadership of the GenStat development in 1985, after John’s retirement from Rothamsted, and glad that John continued as an enthusiastic (although sometimes critical!) user. GenStat embodied John’s originally-very-novel view that statistical programs should provide a programming environment for the development of new methodology. The *procedure* structure introduced in 1987 allowed the resulting new programs to be added to the system as new commands. A good example is the suite of procedures for Lee & Nelder’s hierarchical generalized linear models (see below).

John’s other two major contributions to statistical computing came about while he was Chairman of the Royal Statistical Society’s Working Party on Statistical Computing (1967-1984). The first, in 1968, was the Applied Statistics Algorithms, which aimed to support good computing practice by providing implementations of the basic building blocks of a statistical program. Later much more complicated techniques were added, and the publication of an algorithm for a new piece of methodology became an equally valid (and perhaps more effective) way of registering a new idea. The second contribution was the program GLIM which first appeared in 1974, with 4 further releases up to the final GLIM4 in 1993. This implemented Nelder & Wedderburn’s generalized linear models, and led to a dramatic improvement in the quality of statistical analysis allowing unsatisfactory approximate analyses, such as those involving the angular transformation of percentage data, to be discarded. It had an immense influence on the new generation of practical statisticians. For many it provided their first experience of analysing data interactively. It encouraged them to think about each data set, instead of directing it at a black box with a request for “statistics all”. It provided opportunities to investigate a rich set of models, and good diagnostics to assess which one would be most appropriate.

John retired from Rothamsted in 1984 at the age of 60, but continued his research at Imperial College (of Science, Technology, & Medicine, London) where, since 1972, he had been a Visiting Professor. He retired from Imperial College in October 2009. His first task there was to lead the GLIMPSE project (Nelder 1991), which was funded by the UK Government’s *Alvey* programme to produce a knowledge-based front-end for GLIM. The GLIMPSE system provided advice on data validation, data exploration and model selection. However, it seems to have been intended more as a guide for experts, than as a system to provide expert help to novices, and it never achieved the widespread use that it deserved. However, it contained many very interesting and far-sighted ideas and, when it was released in 1989, it was one of the first statistical expert systems to be made available commercially – and perhaps one of the few to deliver what the originators had promised.

John’s other major activity at Imperial College was his collaboration with Youngjo Lee to develop the theory of *hierarchical generalized linear models* (HGLMs); see the papers by Lee & Nelder (1996, 2001, 2006) and the book by Lee, Nelder & Pawitan (2006). The 1996 and 2006 papers were presented as “read papers” at meetings of the Royal Statistical Society; it is impressive to note that John was 81 years old when he and Youngjo presented the 2006 paper. HGLMs aimed to provide satisfactory methods of analysis for non-Normal data when there is more than one source of random variation. John viewed generalized linear models as a way of liberating statisticians from the “tyranny” of the Normal distribution, and was a little bemused to see this same tyranny reestablished in methods that were devised initially to extend generalized linear models. These *generalized linear mixed models* (GLMMs) catered for additional random variation by adding additional Normally-distributed random effects into the linear model of the generalized linear model. John and Youngjo’s new HGLMs extended the methodology to include the beta-binomial, gamma and inverse-gamma distributions, and showed that the *conjugate* HGLMs (namely binomial GLM with additional beta-binomial random effects, or Poisson with gamma, or gamma with inverse gamma) had attractive advantages in their mathematical theory, computing algorithms and philosophical interpretation. HGLMs can be fitted very efficiently by two interlinked generalized linear models. So we have access to a familiar repertoire of model checking techniques, and can base our choice of error distributions on the data rather than on prejudice or software limitations. Furthermore the analysis can still be carried out interactively – always a very important consideration for John.

With John’s many achievements in statistics, it is important not to forget his other interests. He shared a keen interest in gardening with his wife Mary (nee Hawkes), whom he met and married in 1955 while he was at NVRS; they have a son Jan and a daughter Rosalind. John and Mary were also keen birdwatchers, and were two of the three finders of Britain’s first Siberian Thrush (*Zoothera sibirica*); see Andrew, Nelder & Hawkes (1955). John was very proud of his other paper in British Birds (Nelder 1962), which gave a rigorous statistical assessment of the implausibility of the “Hastings Rarities” and provided convincing evidence for their subsequent removal from the British List. Finally he was a very keen musician and a virtuoso piano player, and his musical soirees at his house in Redbourn will be remembered by the attendees with lasting pleasure.

John received many honours during his career. He had a DSc from University of Birmingham, and received an honorary DSc. from Universite Paul Sabatier, Toulouse, in 1981. He was also elected a Fellow of the Royal Society in 1981. He was President of the International Biometric Society from 1978-1979, and was made an Honorary Life Member in 2006. He was President of the Royal Statistical Society from 1985-1986, and was awarded Guy Medals of the Society in Silver in 1977, and in Gold in 2005. He wrote three books and over 120 papers in statistical and biological journals, including two citation classics: the Nelder & Wedderburn (1972) paper on generalized linear models already mentioned, and his paper written with Roger Mead while at NVRS describing their now very widely-used adaptive simplex optimization algorithm (see Nelder & Mead 1965).

More important perhaps is his statistical legacy of general balance, generalized linear models, hierarchical general linear models – and GenStat – which will keep him always in our thoughts.

Roger Payne

Andrew, D.G., Nelder, J.A. & Hawkes, M. 1955. Siberian Thrush on the Isle of May: a new British bird. *British Birds*, 48, 21-25.

Lee, Y., & Nelder, J.A. (1996). Hierarchical generalized linear models (with discussion). *Journal of the Royal Statistical Society, Series B*, 58, 619-678.

Lee, Y., & Nelder, J.A. (2001). Hierarchical generalized linear models: a synthesis of generalised linear models, random-effect models and structured dispersions. *Biometrika*, 88, 987-1006.

Lee, Y. & Nelder, J.A. (2006). Double hierarchical generalized linear models (with discussion). *Appl. Statist.*, 55, 139-185.

Lee, Y., Nelder, J.A. & Pawitan, Y., (2006). *Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood*. CRC Press, London.

McCullagh, P. & Nelder, J.A. (1989). *Generalized Linear Models (second edition)*. Chapman & Hall, London.* *

Nelder, J.A. (1962). A statistical examination of the Hastings Rarities. *British Birds*, 55, 283-298.

Nelder, J.A. (1965a). The analysis of randomized experiments with orthogonal block structure. I Block structure and the null analysis of variance. *Proceedings of the Royal Society, Series A*, 283, 147–162.

Nelder, J.A. (1965b). II Treatment structure and the general analysis of variance. *Proceedings of the Royal Society, Series A*, 283, 163–178.

Nelder, J.A. & Mead, R. (1965). A simplex method for function minimization. *Computer Journal*, 7, 303-333.

Nelder, J.A. (1991). GLIMPSE, a knowledge-based front end for GLIM. In: *IMA Volume in Mathematics and its Applications 36: Computing and Graphics in Statistics *(Ed. A. Buja & P.A. Tukey), pp. 125–131. New York: Springer Verlag.

Nelder, J.A. & Wedderburn, R.W.M. (1972). Generalized linear models. *Journal of the Royal Statistical Society, Series A*, 135, 370–384.

Payne, R. (2004). Algorithms, data structures and languages — the computational ingredients for innovative analysis. In: *Methods and Models in Statistics — In Honour of Professor John Nelder, FRS.* (Ed. N. Adams, M. Crowder, D.J. H and & D. Stephens), 95-118. London: Imperial College Press.

Senn, S. (2003). A Conversation with John Nelder. Statistical Science, 18, 118–131.

John combined a child-like enthusiasm for discovery with an extraordinarily deep algorithmic appreciation of statistics. His enthusiasm for his subject and his passion for music were maintained right throughout his adult life until the moment of his death. He was an inspiration to us all and an unforgettable friend.

I have memories of a stern task-master from my early days at Rothamsted, but also an inspirational statistician with a strong grasp of the practical, particularly in respect of computing. In later years, he was someone who it was a pleasure to talk to, always with enthusiasm for his latest project.

John Nelder was still giving star presentations at conferences in his 70s and 80s. I think the reason he was able to do this is that his key ideas were *unifying* ideas (e.g. GLMs). They opened up seams that he (and others) were able to mine for years to come.

I first met Professor John Nelder at the 2000 IBC of the IBS in San Francisco where I had a chance to talk to him. He was inspirational and a pleasure to talk to. I have had a chance to refer to both his work on Generalized Linear Models and most recently on Hierarchical Generalized Linear Models and their link to GenStat. His work will be referred to by many for many years to come.

As John’s son, I first want to thank Roger for the very full obituary.I wish I could better understand the details of my father’s contributions to the subject!

What I very clearly knew was his ongoing enthusiasm for statistics,music and birdwatching.I will ensure that these are properly represented at his funeral and subsequent commemoration day on October 9th.

John Nelder inspired me from my beginnings in the statistical profession and I owe him a great debt. For me, he made data analysis sing. His ability to synthesize a statistical topic into a coherent theory are without peer. That he replicated this several times is amazing.

I vividly remember his visits to Adelaide to inform us of his latest developments. These were, of course, en route to another birdwatching excursion. We are truly blessed that he was so productive for so many years.

I have very good memories of the

two times Professor Nelder visited Brazil as my guest. In the First Brazilian Scholl on Regression Models, held in 1989, I made an interview with him that was published in the Proceedings.

I am sending my condolencies for

his family.

I can recall as a student first coming across John’s work with Wedderburn and being totally captivated by such an elegant unification of the theory of modelling. This was beautiful mathematics. A great man who contributed so much.

John will be sadly missed by all of those in the statistics profession who share his passion for the discipline. John’s work has inspired me for many years – as I compile notes on the use of linear mixed models, I find myself still referring to many of his papers, most of which seem to have been forgotten in this new age of bioinformatics and the like.

I have such fond memories of afternoon teas in Redbourn which were a wonderful mixture of John’s endless energy and passion for statistics, music and birds and Mary’s warm hospitality, engaging conversation and yummy cakes!

A major contributor to the discipline of statistics, active and interested in it, and life in general, right to the end. A person whose life and achievements are to be celebrated when the sadness over his death has diminished.

He will remain great for a long time. I’ve exchanged only a few e-mail messages with him, during my M. Sc. in Statistics at ESALQ/ University of São Paulo, Brazil. At that time, I was intoxicated with different types of ANOVA Sum of Squares… I guess that he was moved after reading my first message. His explanations always one step ahead of what I was learning and reading in my Linear Models course. He is great!

John’s support when Geoffrey Berry and I joined him at Wellesbourne was invaluable in learning to be a proper statistician. Two particular memories are several scientists coming out of John’s room and straight into mine with the question “What is John suggesting I should do” when I had to sort out the brilliant idea John had partially conveyed; and of course the many mornings we chewed over our latest dvelopments in the simplex minisation routine.

John loved music and played the piano well and enthusiastically as if in a grand concert hall instead of in a living room. Alan Winterbottom,a near neighbour in Redbourn and a violinist, told me of exciting and spontaneous musical evenings with other statisticians. John’s warm humanity surfaced when Alan was dying painfully. Alan phoned me to say how much he had been comforted by John’s visits to his bedside.

I still have vivid memories of John as he, Graham Wilkinson, Margaret Robertson (later Meyer) and myself together developed an early version of Genstat in Adelaide using many trays of punched cards. John had a keen and persuasive insight into the structure of data and the methods for using that structure in its analysis. I owe much of my interest in data structures to John as I changed fields from statistics to manufacturing logistics where it served me very well.

It was with great sadness that I learned of John’s passing. It was not a surprise. On he and Mary’s last visit to us here in Arizona in late 2007 he was already frail and could walk only about 40 yards before having to stop to rest. We still traveled to Patagonia in Southern Arizona to spot a rare type of hummingbird – he saw a host of them. But even as his body was growing frail, his mind and spirit were keen, and his enthusiasm for birding and statistics was undiminished. We always had some adventure when he visited, as our treck down and back up the Angel Trial at the Grand Canyon in 1992, and to Tombstone a few years later. How he and Mary loved to travel! John leaves a great legacy, and will surely be mentioned in histories of statistics that are written centuries from now. I will miss him as a friend and mentor.

I never had the good fortune to meet Prof Nelder, but his work had a great influence on me.

McCullagh and Nelder was my first technical statistics book, as an epidemiology PhD student, and I used Genstat for my PhD. His clear explanations have stayed with me, and I am proud to recycle them to my own students (with attribution!).

Genstat also showed me a way past the more ‘black box’ approach of SPSS and SAS, to data analysis. Thank you, and I’d like to offer your family my condolences.

John Nelder was a big part of my statistical life from the mid 1960s onwards. I first met him when I was a Ph.D. student in Birmingham, and in 1966 he gave me my first job as a statistician at the National Vegetable Research Station. He had just returned from a year in Adelaide and discussed his plans for Genstat with characteristic enthusiasm. I did not contribute much but I hope that I was a valuable sounding board.

He had recently published papers on general balance and was working towards the idea of generalized linear models, both important unifying concepts for the development of statistical software, but especially for enabling us to think about statistical analysis largely free from concern about computational details.

The concept of a data matrix was also very much in his mind. This anticipated the GenStat spreadsheet by many years. He recognized the necessity of organizing data coherently and logically before embarking on sophisticated statistical analysis, and that statistical software needed to provide tools for this.

Naturally I saw less of John after he moved to Rothamsted, but I continued to meet him at conferences and during his visits to Australia. His enthusiasm for good statistical analysis and for developing methodology directly relevant to this, as well his capacity to be enraged by shoddy statistical analysis clearly remained undiminished. I will miss him very much.

Many years ago, John expressed interest in the content of my Inaugural Lecture at Imperial: a great surprise to me at the time because the lecture had nothing to do with statistics and a lot to do with human interaction with computers and the insight that could thereby be gained. As a result, I was greatly honoured that John later worked with my group: among other things, we created a highly interactive and visual means of interacting with Genstat to create a model, in our case of a small structure inside a lamp. Working with John was both stimulating and enjoyable. I shall miss him.

I knew John through his many years of association with NAG, and was always in awe of his simultaneous rigour and humanity. One always took extra care when presenting in front of John, not because one was frightened of him, but because one didn’t want to disappoint him. I shall endeavour to continue to present as if he were still in the room.

John was an enthusiastic member of the Oxford and Cambridge Musical Club for 33 years. His choice of repertoire was always enterprising. In December 1990 he performed the Walton Sinfonia Concertante with the club orchestra under the baton of Alan Reddish, and it was typical of John that he wanted to play the original fiendishly difficult version of the work before being persuaded to play the simpler revised version.

John was the organiser of the OCMC concert on Feb 2004 at which I was priviliged to join him in the piano duet version of Milhaud’s ‘Boeuf sur le Toit’. His last performance at the club was of the Haydn F minor variations on 11 July 2009.

John was a superb musician and will be sorely missed by his many friends at the OCMC.

I first met John at the International Statistical Modelling Workshop at Leuven, Belgium in 2003. The discussions we had on his presentations at that meeting was a good eye-opener. Though died at a ripe age, John would be sadly missed by all those who know him. I join other friends of John the world over to commisserate with his family on his demise. Rest in peace John.